This had some pretty good past exam questions, need to know the qualitative items quite well
Know why we need qualitative analysis
Independent
Parameter and process variance model with stochastic model
Internal Systemic
Know the 3 components
Score against best practice and calibrate to CoV
Extnernal Systemic
Know the different risk categories
Use benchmark similar to internal but select CoV directly
Correlation
Risk sources are independent of each other
Independent: assume independence across lines, weight by liabilities
Internal: base on correlation matrix \(\Sigma\), again weighted by liabilities
External: correlation between each valuation group and risk categories \(\Rightarrow\) then roll up to the risk categories and assume they are independent of each other
Risk Margin
\(\text{Risk Margin} = \underbrace{\mu}_{\text{Expected Loss}} \times \underbrace{\phi }_{\text{CoV}} \times \underbrace{Z_{\alpha}}_{0.67\text{ for the }75^{th}\text{ percentile}}\)
Addiation analysis
Sensitivity, scenario testing
Internal benchmarking, important to know the relationships and consistency, been heavily tested in the past
External benchmarking
Hindsight and mechanical hindsight
Regularity of review
Haven’t done TIA practice questions
Concepts
Calculations
Estimate risk margin for unpaid losses and premium liabilities
Risk margin = 75th percentile - mean (an Australian regulatory standard)
Based on CoV
Need framework because quantitative is not enough, need both quantitative and qualitative measures to examine the uncertainty
Quantitative analysis requires lots of data
Only captures historical risk
Does not capture risk that did not have an episode (of systemic risk) in the experience period
Portfolio for the analysis should be split into reasonably homogeneous groups
Might combine or further split groups from what was used for liability valuation
Balance the practical benefits from large groups vs insight gained from smaller groups
Might want to further split if a LoB has a portion that has significantly more uncertainty than another part (e.g. HO CAT/non CAT)
\(\phi^2 = \underbrace{\phi_{indep}^2}_{\text{Independent Risk}} + \underbrace{\phi_{internal}^2}_{\text{Internal Systemic Risk}} + \underbrace{\phi_{external}^2}_{\text{External Systemic Risk}}\)
Systemic Risk:
Risks that can vary across valuation classes
Qualitative approaches is recommended for systemic risk
Need to make assumptions about the correlation of the different risks
Most quantitative methods are effective for independent risk and past episodes of external systemic risk. But not very effective with internal systemic risk and external systemic risk that has not yet occurred
Good stochastic model will fit away past systemic episodes (e.g. high inflation) while we still want to hold a margin for the future
Outcome dependent significantly on actual episodes of risk, not all potential ones (for systemic risk that was not fitted away)
Model is unlikely to pick up internal systemic risk from the actuarial valuation process
Randomness inherent to the insurance process
Parameter Risk: ability to select correct parameters and appropriate model
Process Risk: randomness e.g. tossing a die
Use stochastic modeling to analyze independent risk
Focus on periods where episodes of systemic risk were non-existent or minimal so to reduce the impact of the historical external episodes and allow us to focus on the independent risk
Model the parameter and process risk together
Ideally the model adequately model away the systemic risk so all that is left is the independent risk
Complexity of the model should be commensurate with the importance of the total risk margin
For small data set, difficult to model away the external systemic risk \(\Rightarrow\) Use as starting point and then add a margin for external systemic risks not in data
Models for outstanding claims liabilities:
Models for premium liabilities:
GLM, bootstrap, Bayesian
Can model frequency and severity CoV then combine
Remove past systemic episodes from the frequency
Adjust for inflation and seasonality for severity
Uncertainty arising from the liability valuation process/actuarial valuation models. E.g. process the actuary goes through to estimate the liabilities
This can be fro sources anywhere along the chain of valuation: Data record/collection/organization (e.g. not collecting the right data; not using the right data) \(\Rightarrow\) Analysis, AJ \(\Rightarrow\) reserve selection (e.g. management overrides actuary’s opinion)
3 components of internal systemic risk:
Specification Error: From not perfectly modeling the insurance process because it’s too complicated or just don’t have the data
Parameter Selection Error: Trend is particularly difficult to measure
Data Error: Lack of data, lack of knowledge of the underlying pricing, u/w, and claim management process, inadequate knowledge of portfolio
Use bench marking technique:
Need to define risk indicators, score them against best practice, map the scores to a CoV
Score Against Best Practice
For each valuation group, assign a score (1-5) for each risk indicator
Specification Error: # of independent models; range of results from model; ability to detect trends
Parameter Selection Error: Identify best predictors; stability of best predictors (or responsive to process change); Predictors used are close to best predictors
Data Error: Knowledge of past processes affecting predictors; Extent, timeliness, consistency, and reliability of information from the business; data is reconciled and has quality control; freq and sev of past misestimation due to revision of data
Assign weight for each risk indicator (can vary by valuation group)
Average the scores using the selected weights
We score the 3 components for each valuation group (OCL and PL) and then roll up the score and assign the average grade for each valuation group to a CoV
Calibrate Score to CoV
Significant amount of judgement supplement by quantitative analysis
CoV \(\in [5\%, 20\%]\)
Analysis of past model performance should aid in estimating the potential variability
Hindsight Analysis: Compare valuation of liabilities at prior point in time to the current view, to gain insight into how a better model can reduce volatility
Mechanical Hindsight: Mechanically do various ex post analysis, and see how prediction error can be reduced; e.g. do a detailed vs crude and see the difference
Additional comments:
Improvement from poor to fair is greater than from fair to good
Longer tail line will have higher CoV due to difficulty in estimating the parameters
Lager liability will have smaller CoV when all else being equal
OCL and OL might not necessarily be on the same scale
PL may have additional uncertainty as it’s for future business
For short tail lines ELR might be sufficient for PL but might not be the best practice for OCL
Can always just add a load on top if justified
Systemic risk that are not internal
We don’t want to only consider actual episodes of systemic risk in the data set
List of risk categories to consider:
Economic and Social Risks: Inflation, social trends
Legislative, Political Risks, Claims Inflation Risks: Change in law, frequency of settlement vs suits to completion, loss trend (Long tail lines)
Claim Management Process Change Risk: Change in process of managing claims e.g. case reserve practice
Expense Risk: Cost of managing a run-off book
Event Risk: natural or man-made CAT (Premium liabilities for property)
Latent Claim Risk: Claim from source not currently considered to be covered
Recovery Risk: Recoveries from reinsurers or non-reinsurers
A handful of these risk categories will dominate the uncertainty for that valuation group
Useful to rank the risk categories in order of impact on the uncertainty of a valuation group
Lots of the above should be something the valuation actuary already discussed with the business and with claims
Use bench marking technique similar to internal systemic risk
Straight up select the CoV, rank the risk in order of importance to help with the selection
Quantitative approach can provide in insight but we need to also consider possible future sources of external systemic risk
Consider risk that affect u/w and risk selection, claims management, expense management, economic/legl environment
Economic and Social Risks:
Inflation; unemployment; GDP growth; interest rates; driving patterns
For inflation we are concern with the systemic shifts not just randomness (randomness is in the indepedent risk)
Legislative, Political Risks, Claims Inflation Risks
All grouped together since each catergory needs to be uncorrelated with each other
Short tail lines: can impact premium if there are sudden shifts in law of inflation
Long tail lines: Current or potential changes to law; medical technology costs; legal costs
Claim Management Process Change Risk:
Reporting patterns; payment patterns; reopen rates
More important to OCL, only impact PL when a change in process change the cost level of claims
Expense Risk:
Claim handling expense and policy maintenance expense
CoV should be small
Event Risk:
Mostly premium risk
Can model from experience, CAT modeling or input from reinsurers
Latent Claim Risk:
Unlikely for most LoB but can be severe
Due to low probability, likely not worth to commit substantial resources to estimate the risk
Recovery Risk:
S&S for non reinsurer
Reinsurers, consider reinsurance contracts in place specifically for reinsurers where a large amount of premium is ceded
Overall
Assumes the 3 main pieces are independent of each other
\(\phi = \sqrt{\phi_{indep}^2 + \phi_{internal}^2 + \phi_{external}^2}\)
Quantitative method to measure correlation can be valuable, however:
Complexity maybe outweigh the benefit
Results heavily influenced by past correlations while future correlation may differ
Difficult to separate past episodes of independent risk and systemic risk
Internal systemic risk cannot be modeled using standard correlation modeling techniques
Likely won’t aligned with our definitions of independent, internal/external systemic risks
Practical guidance:
Just bucket into 0%, 25%, 50%, 75%, 100%, any finer will likely lead to spurious accuracy
Introduce dummy variables and see their impact in each risk/valuation group pair (inflation, unemployment, propensity to suit, freq of CAT, fraud)
Assume independence across liabilities, where \(i\) is the different valuation groups
\(\phi_{indep}^2 = \sum_i (\phi_i w_i)^2 = (\vec{\phi w})(\vec{\phi w})^T\)
\(\phi_{internal}^2 = (\vec{\phi w}) \times \Sigma \times (\vec{\phi w})^T\)
\(\Sigma\) is the correlation matrix
Again the \(\vec{w}\) is the % of total liabilities
We measure the CoV for each risk category for each valuation group
\(\Sigma_c\) is the correlation matrix between valuation groups for each risk category \(c\)
For a given risk category \(c\), the CoV is:
Then assume independence between risk categories:
\(\phi_{external}^2 = \sum \limits_{c \in risk \: category} \phi_{external, c}^2\)
Important to pick risk categories that are likely to be independent of each other
\(\text{Risk Margin} = \underbrace{\mu}_{\text{Expected Loss}} \times \underbrace{\phi }_{\text{CoV}} \times \underbrace{Z_{\alpha}}_{0.67\text{ for the }75^{th}\text{ percentile}}\)
Sensitivity Testing: By varying the CoV and correlations
Scenario Testing: Consider what assumptions need to change in our mid point to eat up the risk margin
Internal Benchmarking: Compare CoVs within between OCL and PL and also with other valuation groups
Independent risk:
Large liability will have smaller CoV due to law of large numbers
Short tail line will have a small CoV as well due to less volatility
Therefore:
Outstanding Claims Liability: \(\phi_{short \: tail} < \phi_{long \: tail} < \phi_{long \: tail, \: small \: book}\)
Premium Liability - Long Tail: OCL > PL \(\Rightarrow\) \(\phi_{OCL} < \phi_{PL}\)
Premium Liability - Short Tail: OCL < PL \(\Rightarrow\) \(\phi_{OCL} > \phi_{PL}\)
Because OCL is small
LoB with significant event risk will have different risk profiles for the PL and OCL
Internal Systemic:
External Systemic:
External Benchmarking: Compare selected CoV with external sources
Such as APRA 2008
Use just as a sanity check, not appropriate to simply take the risk margins from benchmarks
Independent risk CoV depend on the size of liabilities \(\Rightarrow\) Similar sized liability today would represent a small book due to inflation \(\Rightarrow\) Adjust CoV upward
Estimate PL with a scale up factor from OCL
Hindsight Analysis:
Compare the actual results with expected
Blend of all 3 risks
Useful as a guide if the CoVs are reasonable
Mechanical Hindsight:
Value the liabilities today using a mechanical method and repeat with information at older evaluation date
Measure independent risk over stable periods
By using multiple methods you can measure the internal systemic risk
By measuring over long periods of time, you can measure risk from all sources
Full study to support CoV should be done every 3 years
Key assumptions should be examined in the interim:
Emerging trends
Emerging systemic risks
Change in valuation methods
Should consider applying the key steps to any new portfolio